Square Root of 4761
2026-02-28 01:17 Diff
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Last updated on August 5, 2025

If a number is multiplied by the same number, the result is a square. The inverse of the square is a square root. The square root is used in the field of vehicle design, finance, etc. Here, we will discuss the square root of 4761.

What is the Square Root of 4761?

The square root is the inverse of the square of the number. 4761 is a perfect square. The square root of 4761 is expressed in both radical and exponential form. In the radical form, it is expressed as √4761, whereas (4761)^(1/2) in the exponential form. √4761 = 69, which is a rational number because it can be expressed in the form of p/q, where p and q are integers and q ≠ 0.

Finding the Square Root of 4761

The prime factorization method is used for perfect square numbers. Since 4761 is a perfect square, we can use the prime factorization method to find its square root. Other methods, such as the long division method and approximation method, can also be used. Let us now learn the following methods:

  • Prime factorization method
  • Long division method
  • Approximation method

Square Root of 4761 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 4761 is broken down into its prime factors:

Step 1: Finding the prime factors of 4761

Breaking it down, we get 3 x 3 x 23 x 23: 3² x 23²

Step 2: Now we found out the prime factors of 4761. The second step is to make pairs of those prime factors. Since 4761 is a perfect square, the digits of the number can be grouped into pairs. Therefore, √4761 = 3 x 23 = 69.

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Square Root of 4761 by Long Division Method

The long division method is particularly used for perfect and non-perfect square numbers. Let us now learn how to find the square root using the long division method, step by step:

Step 1: To begin with, we need to group the numbers from right to left. In the case of 4761, we need to group it as 47 and 61.

Step 2: Now we need to find n whose square is less than or equal to 47. We can say n is 6 because 6 x 6 = 36, which is less than 47. The quotient is 6, and the remainder is 47 - 36 = 11.

Step 3: Bring down 61 to make the new dividend 1161. Double the quotient (6) to get 12, which will be our new divisor.

Step 4: Find a digit m such that 12m x m is less than or equal to 1161. We find that m is 9 because 129 x 9 = 1161.

Step 5: Since there is no remainder, the quotient is 69. Therefore, the square root of 4761 is 69.

Square Root of 4761 by Approximation Method

The approximation method can be used to confirm the square root of a number. Since 4761 is a perfect square, approximation will confirm the result:

Step 1: We know that 4761 is between 3600 (60²) and 4900 (70²). Therefore, √4761 falls between 60 and 70.

Step 2: Calculate the midpoint: (60 + 70) / 2 = 65. Test squares around this point. Step 3: We find that 69 x 69 = 4761, confirming that the square root of 4761 is 69.

Common Mistakes and How to Avoid Them in the Square Root of 4761

Students do make mistakes while finding the square root, like forgetting about the negative square root or skipping long division steps. Now let us look at a few of those mistakes that students tend to make in detail.

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Problem 1

Can you help Max find the area of a square box if its side length is given as √4761?

Okay, lets begin

The area of the square is 4761 square units.

Explanation

The area of the square = side².

The side length is given as √4761.

Area of the square = side² = √4761 x √4761 = 69 x 69 = 4761.

Therefore, the area of the square box is 4761 square units.

Well explained 👍

Problem 2

A square-shaped building measuring 4761 square feet is built; if each of the sides is √4761, what will be the square feet of half of the building?

Okay, lets begin

2380.5 square feet

Explanation

We can just divide the given area by 2 as the building is square-shaped.

Dividing 4761 by 2, we get 2380.5.

So, half of the building measures 2380.5 square feet.

Well explained 👍

Problem 3

Calculate √4761 x 5.

Okay, lets begin

345

Explanation

The first step is to find the square root of 4761, which is 69.

The second step is to multiply 69 by 5.

So, 69 x 5 = 345.

Well explained 👍

Problem 4

What will be the square root of (4624 + 137)?

Okay, lets begin

The square root is 70.

Explanation

To find the square root, we need to find the sum of (4624 + 137). 4624 + 137 = 4761, and then √4761 = 69.

Therefore, the square root of (4624 + 137) is ±69.

Well explained 👍

Problem 5

Find the perimeter of the rectangle if its length 'l' is √4761 units and the width 'w' is 38 units.

Okay, lets begin

We find the perimeter of the rectangle as 214 units.

Explanation

Perimeter of the rectangle = 2 × (length + width)

Perimeter = 2 × (√4761 + 38) = 2 × (69 + 38) = 2 × 107 = 214 units.

Well explained 👍

FAQ on Square Root of 4761

1.What is √4761 in its simplest form?

The prime factorization of 4761 is 3 x 3 x 23 x 23, so the simplest form of √4761 = √(3² x 23²) = 69.

2.Mention the factors of 4761.

Factors of 4761 are 1, 3, 9, 23, 69, 207, 529, 1587, and 4761.

3.Calculate the square of 69.

We get the square of 69 by multiplying the number by itself, that is 69 x 69 = 4761.

4.Is 4761 a prime number?

4761 is not a prime number, as it has more than two factors.

5.4761 is divisible by?

4761 has many factors; those are 1, 3, 9, 23, 69, 207, 529, 1587, and 4761.

Important Glossaries for the Square Root of 4761

  • Square root: A square root is the inverse of a square. Example: 8² = 64, and the inverse of the square is the square root, that is √64 = 8.
  • Rational number: A rational number is a number that can be written in the form of p/q, where q is not equal to zero, and p and q are integers.
  • Perfect square: A perfect square is a number that is the square of an integer. Example: 64 is a perfect square of 8.
  • Prime factorization: The expression of a number as a product of its prime factors. Example: The prime factorization of 18 is 2 x 3 x 3.
  • Integer: An integer is a whole number that can be positive, negative, or zero. Example: -2, 0, 3, 42 are integers.

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Jaskaran Singh Saluja

About the Author

Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.

Fun Fact

: He loves to play the quiz with kids through algebra to make kids love it.